MixIT [1]} has proven its effectiveness under various self-supervised speech enhancement settings [2]}, [3]}. Specifically, MixIT assumes that the training dataset consists of two portions \(({\cal D}_m, {\cal D}_n)\) , where \({\cal D}_m\)  is the part of the dataset which carries mixtures of speech and one noise source while \({\cal D}_n\)  contains isolated noise recordings. During training, a new batch of artificial mixtures of mixtures (MoMs) is generated, \({\mathbf {x}}= \mathbf {s}+ \mathbf {n}_1 + \mathbf {n}_2\) , by sampling a batch of noisy speech recordings \(\mathbf {m}\sim {\cal D}_m\)  and a batch of clean noise samples \(\mathbf {n}_2 \sim {\cal D}_n\) , where \(\mathbf {m}=\mathbf {s}+ \mathbf {n}_1\) . The separation model always estimates \(M=3\)  sources (\(\widehat{\mathbf {s}}, \widehat{\mathbf {n}}_{1}, \widehat{\mathbf {n}}_{2}= f_{\mathcal {S}}({\mathbf {x}}; {\mathbf {\theta }_{\mathcal {S}}})\) ) and the following permutation invariant loss function is minimized for the \(b\) -th input MoM:
\(\begin{aligned}\mathcal {L}_{\operatorname{MixIT}}^{(b)} =\underset{\pi \in \Pi _{2,3}}{\min }\left[ {\cal L}(\widehat{\mathbf {s}}_b + \widehat{\mathbf {n}}_{\pi _1, b}, \mathbf {m}) + {\cal L}(\widehat{\mathbf {n}}_{\pi _2, b}, \mathbf {n}_{2, b}) \right], \forall b.\end{aligned}\) 
